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Extended Phase Space Mechanics
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24-hour satellite Accordingly Appendix approximation arc sin(ksnW argument of pericenter argument of perigee ascending node barred elements barred variables barycenter canonical transformation Cartesian Chapter considered constant cos(S cosf cosl defined derived e.cos(f eccentric anomaly elliptic integral equatorial ellipticity esinE expansion expression extended phase space Geocentric Geometry geopotential gives Hamilton's equations Hence ideal resonance inclination independent variable initial value Kamel Keplerian elements libration librational period Lie series linear long-period behavior long-period motion lunar mean lunisolar perturbations mean anomaly mean motion modified Delauney similar momenta Newton-Raphson normalized numerically integrated oblateness obtained orbital orbital eccentricity order of magnitude oscillation periodic terms perturbation solution perturbing potential Poincare system Poincare variables power series procedure produces quantities relation relationship result seen semilatus rectum semimajor axis sinE sinf solar mean tesseral harmonic third-body tion true anomaly true longitude two-body unperturbed motion